Fractional modified Korteweg de Vries equationModified G '/G-expansion methodAll applications of fractional calculus to physics propose fractional equations of motion for various complex phenomena. Complex and nonlinear fractional equations are very familiar and often occur in nature. Therefore, the ...
KlausBrauer:TheKorteweg-deVriesEquation2 solitaryelevation,arounded,smoothandwell-definedheapofwater,whichcontinuedits coursealongthechannelapparentlywithoutchangeofform or diminution of speed. I followed it on horseback, and overtook it still rolling on at a rate of some eight or nine miles an hour,...
Let us now work on building the most efficient system of one-dimensional subalgebras for the equation denoted by (1.6). This process will allow us to simplify the equation and find solutions that are invariant under certain groups. We will be following the procedure outlined in the reference p...
CAS Application to the Construction of the Collocations and Least Residuals Method for the Solution of the Burgers and Korteweg–de Vries–Burgers EquationsComputer algebra systemKorteweg–de Vries–Burgers equationderivation of the formulas of the analytic-numerical algorithm...
Chen, Weakly nonlinear wavepackets in the Korteweg-de Vries equation: The KdV/NLS connection, Math. Comput. Simulation (2001), to appear.J.P. Boyd and G.-Y. Chen. Weakly nonlinear wavepackets in the Korteweg-de Vries equation: the KdV/NLS connection, Mathematics and Computers in Simulation...
LawsNonlinearEvolutionEquationsWith the aid of Mathematica, new exact travelling wave solutions for fifth-order KdV equation are obtained by using the solitary wave ansatz method and the Wu elimination method. The derivation of conservation laws for a fifth-order KdV equation is considered.Elham M. ...
Derivation and Implicit Solution of the Harry Dym Equation, and Its Connections with the Korteweg-De Vries EquationWave equationsSolutions(General)WavesTHe Harry Dym equation, which is related to the classical string problem, is derived in three different ways. An implicit cusp solitary wave solution...
In this paper we show how approximate scheme can be used to solve the fKdV equation and generate uniform forced solitons. A detail derivation of the approximate solution was provided and various profiles of fKdV such as the depth of depression zone; hd, amplitude; as, speed; s and the ...
Derivation of Korteweg-de Vries flow equations from third order nonlinear Schröodinger equation.The nonlinear Shrdinger equation with a third-order dispersive terms is considered. We perform a multiple scales analysis on the third order nonlinear Schrdinger equation and their corresponding Hamiltonian ...
KdV equationMultiple scalesHamiltonianWe perform a multiple scales analysis on the modified nonlinear Schrdinger (MNLS) equation in the Hamiltonian form. We derive, as amplitude equations, Korteweg–de Vries (KdV) flow equations in the bi-Hamiltonian form....